Question: The first four Hermite polynomials are 1, 2 x , 4 x^ 2 2, 8 x^ 312 x . These polynomials arise in many fields:

The first four Hermite polynomials are 1, 2x, 4x^2 2, 8x^312x. These polynomials arise in many fields: signal processing, physics, numerical analysis, probability, combinatorics, etc. Show that the first four Hermite polynomials form a basis ofP3

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